g level of unbalanced rotating member 2

[fetterlabs]

I have what I thought was a simple question, but am having difficulty obtaining an answer. Hopefully you all can help.

If an accelerometer were mounted so it could measure the normal acceleration of a perfectly balanced rotating shaft it would read zero. Now take that same shaft and make it unbalanced by adding mass at a point. The frequency of the vibration will be 1 X RPM but how does the mass affect the amplitude? Is there an equation that relates the amount of imbalance to the amplitude of the acceleration?

JLF

 

[EnglishMuffin]

1. What do you mean by the "normal acceleration" of a rotating shaft ? If you mean the radial acceleration at some point on the surface, it's certainly not zero. I expect you mean the acceleration of a point on the shaft axis.
2. How does the mass affect the amplitude ? It depends on the shaft stiffness as well as the mass. What you are probably after is the basic "whirling" equation, which is:

r = m*omega^2*e/(k*gc-m*omega^2)

where r = lateral deflection
e = mass eccentricity
m = imbalance mass (which will include some portion of the shaft mass as well as the added mass)
omega = angular velocity (rad/sec)
k = lateral stiffness of shaft at the mass location
gc = unit multiplier (for unit consistency)

In reality, things are usually much more complicated, and you need to study texts on rotordynamics.

 

[EnglishMuffin]

Actually, on second thoughts, I've confused the issue a bit - just think of m as the added imbalance mass and the shaft itself as being massless. That should do for a start anyway.

 

[fetterlabs]

EnglishMuffin,
1. Some call it radial acceleration, I prefer normal. I mean perpendicular to the surface. If you ignore the steady-state acceleration due to gravity and only measure the acceleration due to rotation, in a perfectly balanced shaft it should be zero.

In reality, things are usually much more complicated, and you need to study texts on rotordynamics.

I realize this, but I trying to develop a simple model. Thanks for the assistance.

 

[alexit]

I was very confused...the acceleration (measured in units of gravity) is not equal to the lateral deflection.

Take the distance from CG of the total (including the eccentricity), relative to the axis of rotation. This is distance. Take revolutions per second and determine centrifugal force from the relative eccentric mass at this distance.

F=ma gives you the MAX acceleration (total mass here not relative eccentric mass) this eccentric mass would output to the accelerometer (not counting damping, assuming rigid shaft.)

Alex

 

[EnglishMuffin]

fetterlabs: I'm afraid you've completely lost me. I don't know what you mean by "Ignore the steady state acceleration due to gravity", unless your shaft happens to be in free fall. And the acceleration normal to the surface of a finite sized rotating shaft, whether imbalanced or not, is not zero.

 

[electricpete]

I would like to hear the original question clarified. What are you really trying to figure out? Are you trying to relate level of unbalance to level of vibration which may be measured on a bearing housing or shaft prox probe (expressed in g's)?

=====================================
Eng-tips forums: The best place on the web for engineering discussions.

 

[EnglishMuffin]

Yes, I agree that would help - my comments were getting a little facetious.

 

[EnglishMuffin]

And I suppose in the spirit of electricpete's post, I could perhaps add the following:
In the case of a prox probe mounted near the imbalance mass, then taking k to be the combined effective shaft and bearing stiffness, and ignoring shaft and bearing damping, then, to a first order of approximation, the maximum displacement amplitude output from the prox probe would be given by r from the equation in my first post. You could convert this to acceleration in g's by multiplying it by omega^2/gc, where gc depends on your unit system. In the case of an accelerometer mounted on the outer race of one of the bearings, you would have to know the bearing-to-housing stiffness, and it would also be highly affected by damping. In other words, it would be almost impossible to predict theoretically in advance.

 

[fetterlabs]

Thank-you alexit for boiling it down to a case of uniform circular motion for me.

As for electricpete and EnglishMuffin:

There are two basically two types of accelerometers. Steady-state accelerometers will measure from DC to several hundred hertz. Dynamic accelerometers measure from a few hertz to several thousand hertz.

Now let's say I have a magic rotating shaft that is perfectly balanced. It's connected to the rest of the world with massless, frictionless bearings. On the top of the massless, frictionless bearings I mount a steady-state accelerometer and a dynamic accelerometer. Through more magic I make the shaft spin. The steady-state accelerometer will read the acceleration due to gravity, or 1g. The dynamic accelerometer has no DC response so it will read 0g. Now I imbalance my shaft and spin it again. The steady-state accelerometer will read gravity + the acceleration due to the imbalance. The dynamic accelerometer will read just + the acceleration due to the imbalance. Since I trust that gravity is going to be around for awhile, I posed the question using a dynamic accelerometer since I'm only interested in the acceleration due to the imbalance.

 

[jclough]

I hope i understand your question but here goes...

The unbalance mass affects the vibration sensed by your accelerometer directly based on an influence coefficient related to the stiffness of the structure supporting the rotor. The amount of vibration produced by any unbalance depends of how stiff the supporting structure is.

If you change the speed, vibration will increase by the change in the speed squared provided that the supporting structure stiffness remains constant and your not near or at any point of resonance. Keep in mind that you must consider the resonant frequency of the supporting structure, the rotor and/or the entire assembly depending on how its mounted. Fc=U*RPM2.

You can coorelate unbalance to vibration. You'll need to do some tests with known test masses and come up with influenc e coefficients. If you need to know how to do this with real world parts that don't have any magic..contact me and I'll show you how to get through it.

 

[EnglishMuffin]

fetterlabs: sorry, but I have never heard of such a thing as a "steady state accelerometer" which "reads the acceleration due to gravity", but perhaps your terminology is the problem.
Zhivotov: my equation is not "erroneous" and can be found in "Vibration Theory and Applications" by Thomson, among other places.
I think I will have to pass on any future responses on this thread.

 

[fetterlabs]

EnglishMuffin:sorry, but I have never heard of such a thing as a "steady state accelerometer" which "reads the acceleration due to gravity"


I think you need to get out more.

 

[EnglishMuffin]

Well, there are such things as accelerometers which are more suited to low frequency work, sometimes referred to as "Steady State", but I am not aware of any that will "read the acceleration due to gravity", at least while stationary. But perhaps someone else can enlighten me. However, I agree that I do need to get out more! That's positively my final response.

 

[MikeyP]

EnglishMuffin,

This was the second hit on Google for the search term - accelerometer DC.

http://www.engineeringtalk.com/news/tec/tec102.html

I have seen one but never used one. I understand you can do a quick field calibration simply by turning the thing over.

M

--
Dr Michael F Platten

 

[fetterlabs]

The 7290 series is very good. Here are some others.

http://www.msiusa.com/download/pdf/english/icsensors/accelerometers/stand_alone/model_3140.pdf

http://www.pcb.com/product.asp?measureType=852&productType=&template_id=56&showProduct=1

 

[electricpete]

acceleration predicted by Funbalance = ma is of course not the max acceleration. It is only correct for high frequencies far above resonance/critical where the system is mass controlled. Closer to resonant frequencies acceleration can get much higher. At frequencies far below resonance the system will be stiffness controlled and vibration will be independent of mass (as long as resonant frequency remains far above operating speed).

Yuriy (along with others) has given you a good explanation and equations. Yuriy's equation is in agreement with Den Hartog. Pick a region above or below resonance. Solve for his "a"=displacement. Multiply by W^2 to get acceleration. By the way his MW** means M*W^2.

Thanks for the unsolicited tutorial on gravity and accelerometers. I for one just asked for clarification on a post that remains vaguely posed. But I see you have discovered what you apparently were missing (F=ma)

=====================================
Eng-tips forums: The best place on the web for engineering discussions.

 

[EnglishMuffin]

MikeyP: You seem to have missed the point of my response. I am perfectly well aware of such accelerometers, but I am not aware of any that will produce a meaningful output of 1g while being subject to no acceleration whatsoever, as fetterlabs seems to be claiming in his third post. Of course, you could artificially adjust the DC offset such that this was the case, but why you would want to pretend that an object which is stationary relative to the surface of the earth is accelerating at 1g is beyond me.

 

[electricpete]

em - if you could calibrate your instrument to read zero g's with that accell in one orientation, it would read 2g's when you turned it upside down.

Safe to say the original comment
("If you ignore the steady-state acceleration due to gravity and only measure the acceleration due to rotation, in a perfectly balanced shaft it should be zero.&quot was flat wrong. There was no discussion of accelerometers there, only discussion of acceleration which was plainly incorrect (unless this rotor happens to be in a freefall). EM was right to question this ridiculousness.

=====================================
Eng-tips forums: The best place on the web for engineering discussions.

 

[EnglishMuffin]

Thanks electricpete - I was beginning to wonder if I had contracted Kreutzfeld-Jacob disease or something. And now I really am going to shut up!